How to have equal size faces
I don't know if you have a reason to make your loops exactly equidistant, if so, I've missed, with this one.. This is really to reduce geometry, while preserving curvature.
Enable the shipped Add-on 'Simplify Curves' and..

Select, duplicate, and make a new object of one vertical half-loop from your cone (BTW, straighten it out in your chosen plane, and make sure it has verts at directly above and below the object origin)
Convert the profile to a Curve
Call up 'Simplify Curve' from your F3 search menu and tweak to acceptable preservation of curvature
Convert the profile back to a mesh, and Screw modifier turn it back into a cone.


You can save a lot of polygons..

Without that much difference in curvature .. (both examples subdivided once) and if you want to keep the shape flexible, Curves can be given a Screw modifier, before conversion.
This .blend includes some discretionary manual edits to the profile just before spinning .. bevelling vertices at very sharp corners to hold up under subdiv. The simplifying step is from 'Plane_005' to 'Simple_Plane_005'.